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When I run a multiple regression analysis in Excel on 20 independent variables and 1 dependent variable (in two goes), I obtain in the summary a set of p-values. When I select the (six) ones that are less than 0.25 and then rerun the multiple regression analysis, the p values are smaller than they were previously. Shouldn't the p values be the same?? I would have thought that the p-values should be the same as each time an individual regression is run against the dependent variables?

Otherwise could someone please point out my misunderstanding of multiple regression analysis and explain/justify why these p-values are smaller.

Trajan
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    See also also [Is there a difference between 'controlling for' and 'ignoring' other variables in multiple regression?](http://stats.stackexchange.com/q/78828/17230), [Should covariates that are not statistically significant be 'kept in' when creating a model?](http://stats.stackexchange.com/q/66448/17230), & [How can adding a 2nd IV make the 1st IV significant?](http://stats.stackexchange.com/q/28474/17230). – Scortchi - Reinstate Monica Jan 22 '16 at 14:55
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    I'd look at the magnitude of the estimated effect (the coefficient) and the corresponding standard error for each of the six terms in the reduced (selected) model and the "original" *p* value. Both will have changed, and in particular the standard errors will tend to be smaller; this is the bias variance trade-off at work. Anyway, those *p* values you quote are conditional upon the other terms in the model; change the other terms in the model, change the *p* value. – Gavin Simpson Jan 22 '16 at 14:56

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